Slope-intercept form for the line that passes through (10, 5), and is perpendicular to the graph of 5x + 4y = 8

Let us convert this equation from standard to slope intercept form first.

5x+4y=8

4y=-5x+8

y=-5/4x+2

For the other line to be perpendicular it has to have an opposite reciprocal slope. That would be 4/5. This will make the equation for the new line "y=4/5x+b". We just need to find the y-intercept. Using the point given...

5=4/5(10)+b

5=8+b

b=-3

y=4/5x-3

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope

c = intercept

The equation of the given line is

5x + 4y = 8

Rearranging the equation so that it looks like the slope intercept form, it becomes

4y = -5x + 8

y = -4/5 + 8/4

y = - 4/5/+ 2

Slope, m = -4/5

For two lines to be perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. It means that the slope of the line perpendicular to the given line is 5/4.

The line passes through (10, 5). We would determine the intercept by substituting m = 5/4, x = 10 and y = 5 into y = mx + c. It becomes

5 = 5/4 × 10 + c

5 = 25/2 + c

c = 5 - 25/2 = -15/2

The equation becomes

y = 5x/4 - 15/2

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